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A notion of localization of information within quantum subsystems plays a keyrole in describing the physics of quantum systems, and in particular is aprerequisite for discussing important concepts such as entanglement andinformation transfer. While subsystems can be readily defined for finitequantum systems and in local quantum field theory, a corresponding definitionfor gravitational systems is significantly complicated by the apparentnonlocality arising due to gauge invariance, enforced by the constraints. Arelated question is whether "soft hair" encodes otherwise localizedinformation, and the question of such localization also remains an importantpuzzle for proposals that gravity emerges from another structure such as aboundary field theory as in AdS/CFT. This paper describes different approachesto defining local subsystem structure, and shows that at least classically,perturbative gravity has localized subsystems based on a split structure,generalizing the split property of quantum field theory. This, and relatedarguments for QED, give simple explanations that in these theories there islocalized information that is independent of fields outside a region, inparticular so that there is no role for "soft hair" in encoding suchinformation. Additional subtleties appear in quantum gravity. We argue thatlocalized information exists in perturbative quantum gravity in the presence ofglobal symmetries, but that nonperturbative dynamics is likely tied to amodification of such structure.

How is quantum information localized in gravity?